Mix breadcrumbs, oil, mustard, shallot, lemon juice, capers and thyme in a small bowl until combined.

Working with one at a time, spread 1teaspoon mayonnaise on a salmon strip. Spread about 3 tablespoons of the breadcrumb mixture over the mayonnaise. Starting at one end, roll the salmon up tightly, tucking in any loose filling as you go. Insert a toothpick though the end to keep the pinwheel from unrolling. Place in the prepared dish. Repeat with the remaining salmon strips.

Bake the pinwheels until just cooked through, 15 to 20 minutes. Remove the toothpicks before serving.